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Quantum Inverse Scattering Method and Correlation Functions

TL;DR: In this article, a detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well as main models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models.
Abstract: The book contain detailed explanation of Bethe Ansatz, Quantum Inverse Scattering Method and Algebraic Bether Ansatz as well. Main Models are Nonlinear Schrodinger equation (one dimensional Bose gas), Sine-Gordon and Thiring models. Heisenberg Antiferromagnet and Hubbard models. It is explained in detail, how to calculate correlation functions.
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Journal ArticleDOI
TL;DR: In this article, the properties of entanglement in many-body systems are reviewed and both bipartite and multipartite entanglements are considered, and the zero and finite temperature properties of entangled states in interacting spin, fermion and boson model systems are discussed.
Abstract: Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.

3,096 citations

Journal ArticleDOI
17 Apr 2008-Nature
TL;DR: It is demonstrated that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription, and it is shown that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki.
Abstract: It is demonstrated that an isolated generic quantum many-body system does relax to a state well described by the standard statistical mechanical prescription The thermalization happens at the level of individual eigenstates, allowing the computation of thermal averages from knowledge of any eigenstate in the microcanonical energy window An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive Recently, meaningful experimental studies1,2 of the problem have become possible, stimulating theoretical interest3,4,5,6,7 In generic isolated systems, non-equilibrium dynamics is expected8,9 to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible10 For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete11 Some recent studies4,5 even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems Here we demonstrate that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch12 and Srednicki13 A striking consequence of this eigenstate-thermalization scenario, confirmed for our system, is that knowledge of a single many-body eigenstate is sufficient to compute thermal averages—any eigenstate in the microcanonical energy window will do, because they all give the same result

2,598 citations


Cites background from "Quantum Inverse Scattering Method a..."

  • ...Thus, although at least some constraints other than the conservation of energy must be kept, it turns out that only a relatively limited number of additional conserved quantities with functionally independent expectation values are needed; adding further ones is redundant....

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Journal ArticleDOI
TL;DR: In this article, the authors review recent developments in the physics of ultracold atomic and molecular gases in optical lattices and show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics.
Abstract: We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed. Motto: There are more things in heaven and earth, Horatio, Than are dreamt of in your...

1,535 citations


Cites methods from "Quantum Inverse Scattering Method a..."

  • ... properties of different bipartite partitions. Analytical and numerical methods often rely on the size and dimensionality of the system. Powerful techniques like bosonization [46,48,232], Bethe ansatz [233,234,45], Jordan–Wigner transformation [154,235], or the mentioned DMRG exist and allow to solve some paradigmatic one dimensional systems, such as for instance Heisenberg spin 1/2, XXZspin chains, or 1D Hubb...

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Journal ArticleDOI
TL;DR: In this article, a one-dimensional scattering amplitude and effective 1D interaction potential for atoms confined transversally by an atom waveguide or highly elongated ''cigar''-shaped atomic trap was calculated.
Abstract: We calculate, within the pseudopotential approximation, a one-dimensional scattering amplitude and effective one-dimensional interaction potential for atoms confined transversally by an atom waveguide or highly elongated ``cigar''-shaped atomic trap. We show that, in the low-energy scattering regime, the scattering process degenerates to a total reflection, suggesting an experimental realization of a famous model in theoretical physics---a one-dimensional gas of impenetrable bosons (``Tonks'' gas). We give an estimate for suitable experimental parameters for alkali atoms confined in waveguides.

1,481 citations

Journal ArticleDOI
20 May 2004-Nature
TL;DR: A theoretical prediction of the momentum distribution is made based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.
Abstract: Strongly correlated quantum systems are among the most intriguing and fundamental systems in physics. One such example is the Tonks-Girardeau gas, proposed about 40 years ago, but until now lacking experimental realization; in such a gas, the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system. In order to minimize their mutual repulsion, the bosons are prevented from occupying the same position in space. This mimics the Pauli exclusion principle for fermions, causing the bosonic particles to exhibit fermionic properties. However, such bosons do not exhibit completely ideal fermionic (or bosonic) quantum behaviour; for example, this is reflected in their characteristic momentum distribution. Here we report the preparation of a Tonks-Girardeau gas of ultracold rubidium atoms held in a two-dimensional optical lattice formed by two orthogonal standing waves. The addition of a third, shallower lattice potential along the long axis of the quantum gases allows us to enter the Tonks-Girardeau regime by increasing the atoms' effective mass and thereby enhancing the role of interactions. We make a theoretical prediction of the momentum distribution based on an approach in which trapped bosons acquire fermionic properties, finding that it agrees closely with the measured distribution.

1,341 citations